What is the amplitude, period, phase shift and vertical displacement of #y=-2cos2(x+4)-1#?

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Answer 1 · 2017-11-28T00:43:57

See below.

Amplitude:

Found right in the equation the first number:

#y=-ul2cos2(x+4)-1#

You can also calculate it, but this is faster. The negative before the 2 is telling you that there will be a reflection in the x axis.

Period:

First find k in equation:

#y=-2cosul2(x+4)-1#

Then use this equation:

#period=(2pi)/k#

#period= (2pi)/2#

#period= pi#

Phase Shift:

#y=-2cos2(x+ul4)-1#

This part of the equation tells you that the graph will shift left 4 units.

Vertical Translation:

#y=-2cos2(x+4)ul(-1)#

The -1 tells you that the graph will shift 1 unit down.